boolean-logicboolean-operationsboolean-algebra

If p → q then q → p?


I'm trying to get back into boolean algebra after many years without it, I'm currently working on an exercise that asks to verify if p → q or q → p are tautologies, p and q being very long expressions hard to simplify, yet p → q is very easy to prove a tautology using a truth table while q → p takes a lot longer to verify using a truth table.

Is the statement p → q ≡ q → p correct? I can't find concise info on this proposition but building the truth table makes it seem like it is correct.

If it is I could answer that since p → q is a tautology q → p is too.


Solution

  • When I understand your question right, then a look at the truth-table shows the following:
    a -> b = c | b -> a = c
    0 -> 0 = 1 | 0 -> 0 = 1
    0 -> 1 = 1 | 0 -> 1 = 0
    1 -> 0 = 0 | 1 -> 0 = 1
    1 -> 1 = 1 | 1 -> 1 = 1
    This show that a->b is not euqal to b->a.
    I hope this help a little bit.